Average Error: 0.1 → 0.1
Time: 23.3s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\log \left(\sqrt{y}\right) \cdot x + \left(\left(\log \left(\sqrt{y}\right) \cdot x - z\right) - y\right)\]
\left(x \cdot \log y - z\right) - y
↓
\log \left(\sqrt{y}\right) \cdot x + \left(\left(\log \left(\sqrt{y}\right) \cdot x - z\right) - y\right)
double f(double x, double y, double z) {
        double r2412487 = x;
        double r2412488 = y;
        double r2412489 = log(r2412488);
        double r2412490 = r2412487 * r2412489;
        double r2412491 = z;
        double r2412492 = r2412490 - r2412491;
        double r2412493 = r2412492 - r2412488;
        return r2412493;
}
↓
double f(double x, double y, double z) {
        double r2412494 = y;
        double r2412495 = sqrt(r2412494);
        double r2412496 = log(r2412495);
        double r2412497 = x;
        double r2412498 = r2412496 * r2412497;
        double r2412499 = z;
        double r2412500 = r2412498 - r2412499;
        double r2412501 = r2412500 - r2412494;
        double r2412502 = r2412498 + r2412501;
        return r2412502;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(x \cdot \log y - z\right) - y\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.1

    \[\leadsto \left(x \cdot \log \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} - z\right) - y\]

  4. Applied log-prod0.1

    \[\leadsto \left(x \cdot \color{blue}{\left(\log \left(\sqrt{y}\right) + \log \left(\sqrt{y}\right)\right)} - z\right) - y\]

  5. Applied distribute-rgt-in0.1

    \[\leadsto \left(\color{blue}{\left(\log \left(\sqrt{y}\right) \cdot x + \log \left(\sqrt{y}\right) \cdot x\right)} - z\right) - y\]

  6. Applied associate--l+0.1

    \[\leadsto \color{blue}{\left(\log \left(\sqrt{y}\right) \cdot x + \left(\log \left(\sqrt{y}\right) \cdot x - z\right)\right)} - y\]

  7. Applied associate--l+0.1

    \[\leadsto \color{blue}{\log \left(\sqrt{y}\right) \cdot x + \left(\left(\log \left(\sqrt{y}\right) \cdot x - z\right) - y\right)}\]

  8. Final simplification0.1

    \[\leadsto \log \left(\sqrt{y}\right) \cdot x + \left(\left(\log \left(\sqrt{y}\right) \cdot x - z\right) - y\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  (- (- (* x (log y)) z) y))